1. Introduction to Spin Coating and Derivation of a Simple Model
Presented By: Katie Weigandt
Good afternoon.
Introduction
More specifically I will introduce you all to spin coating and then discuss the derivation of an equation modeling the retention of liquid on a spinning disk.

2. Agenda Introduction to spin coating Physics of spin coating
Definition and brief history of spin coating
Uses of spin coating technology
Common spin coating defects
Physics of spin coating
Basic physics behind spin coating
The Spinning Disk Problem
Further work on spin coating in relation to my honors college thesis
I’ll begin with an introduction to spin coating:
What is spin coating?
Why is it important and where is it used?
And because of the importance of uniform and defect free films in industries in which spin coating is used I will discuss some common spin coating defects.
Then I will discuss:
Physics of spin coating and the “Spinning Disk Problem”
Finally I will introduce you all to what I will be working on for my honors college thesis and show how it relates to the presentation I have given today.

3. What is Spin Coating?
A process in which solution is spread evenly over a surface using centripetal force.
Spin coating will result in a relatively uniform thin film of a specific thickness.
Spin coating is an important way of creating thin films in the microelectronics industry.
Spin coating is a process in which a liquid is spread over a flat uniform surface through centripetal forces.
As the surface continues to spin the film gets more and more thin and approaches an asymptotically thin height.
The result of spin coating is a uniform thin film on the surface of the wafer. In the case of an oil or lubricant the film will remain liquid. If the deposited material is a polymer in solvent, the solvent will evaporate, leaving a solid film on the substrate.

4. Brief History of Spin Coating
Spin coating was first used to apply coatings of paint and pitch around seventy years ago.
In 1958 Emslie et. al. developed the first spin coating model.
This model has been used as a basis for future more specific or complicated models.
Lawrence and Zhou: “Spin Coating of Non-Newtonian Fluids”

5. Spin Coater Schematic Wafer is held to chuck with vacuum pump.
Basin
Lid
Wafer is held to chuck with vacuum pump.
Lid is placed over spinning basin before spin is initiated.
This is a general schematic of a spin coater.
A spin coater has a chuck on which a wafer is held by vacuum.
The chuck spins causing the centripetal force which creates the thin film. The excess solution is thrown off the wafer into the basin.
A lid is place on top of the spin coater to prevent splashing of solution and as a safety consideration in case the vacuum fails.
The lid in the spin coater located in Gleeson has a hole in the center which allows for dynamic addition of the solution to the wafer.

6. Basic Physics of Spin Coating
Centripetal force is responsible for the spread of liquid across the wafer.
A liquid of an assumed initial thickness H0 is placed on the wafer.
As the wafer begins to spin centripetal forces cause the liquid is spread out and then become thin on the wafer as demonstrated by this animation.
If the substrate is spun indefinitely then eventually the rate of thinning will become negligible and a final thin film will be created.
At long times the fluid will flow only negligibly, resulting in a lower limit of the final thickness.

7. Industrial Uses of Spin Coating
Photoresist for patterning wafers in microcircuit production.
Insulating layers for microcircuit fabrication such as polymers.
Flat screen display coatings.
Antireflection coatings and
conductive oxide.
DVD and CD ROM
Television tube
antireflection coatings.
Spin coating is used in a number of industries where it is necessary to create thin films.
Spin coating processes are used in the microelectronics industry to coat wafers with photoresist which allow already existing layers on the wafer to be selectively etched.
Spin coating is also used to apply thin layers of polymers to wafers for various steps through out the manufacture of processed wafers.
Spin coating is also used to apply coatings to DVD and CD ROMs as well as Displays and television tubes.

8. Common Spin Coating Defects
Bubbles on the surface of the coated wafer.
This occurs when fluid is deposited as the wafer is spinning, and may be caused by a faulty dispense tip.
A swirling pattern may be observed.
Causes:
Fluid deposited off center
Acceleration too high
Spin time to short
Exhaust rate too high
It is important in the microelectronics industry that each layer be uniform and defect free. So I will discuss some defects that can occur in spin coating and possible causes of those defects.
The first defect we will discuss is bubbles observed on the coating surface. Bubbles will disrupt the uniformity over the surface of the wafer. They may be caused by a faulty dispenser during dynamic deposition of coating solution.
A swirling pattern may occur if the angular acceleration is too high, if the spin time is not long enough or if the fluid is deposited off center. It can also be caused by too great of a solvent exhaust rate.

9. Common Spin Coating Defects
A mark or circle in the center of the wafer could indicate a chuck mark.
If a chuck mark occurs the type of chuck should be changed.
Streaks can occur on the wafer for a number of reasons including:
Acceleration too high
Fluid deposited off center
Particles on surface prior to spin

10. Common Spin Coating Defects
Uncoated areas on wafer occur when to little fluid is deposited on the wafer.
Pinhole defects can be caused by:
Air bubbles
Particles in fluid
Particles on substrate.
When my group did spin coating we had both of these problems when spin coating our unknown.

11. Agenda Introduction to spin coating Physics of spin coating
Definition and brief history of spin coating
Uses of spin coating technology
Common spin coating defects
Physics of spin coating
Basic physics behind spin coating
Derivations of common spin coating models
Further work on spin coating in relation to my honors college thesis
Moving on to a more in depth explanation of the spin coating process and derivation of a simple model used to relate film thickness to time for spin coating of Newtonian fluids.

12. Spin Coating Process Four main processing steps:
Step 1: Deposit fluid onto substrate.
Step 2: Accelerate wafer to final radial velocity.
The spin coating process can be discussed in three stages. We will consider the process in which the fluid is deposited prior to the wafer spinning.
The first step is to apply a known amount of solution to the wafer.
The substrate then begins to spin and accelerates until it reaches its final spinning velocity. During spin up, a large amount of excess solution is removed from the wafer.

13. Spin Coating Process Four main processing steps:
Step 3: The coating thins at a rate that depends on the velocity at which the wafer is spinning and the viscosity of the fluid.
Step 4: Solvent is evaporated from the film, resulting in further thinning.
The third step in the spin coating process is to continue spinning the wafer at constant velocity.
During this time centripetal forces will result in gradual thinning of the fluids.
At some point the liquid will flow negligible and then the primary film thinning mechanism is evaporation of the solvent from the film. Once the solvent has evaporated a solid thin film will remain.

14. The Spinning Disk Problem
Consider unsteady behavior of liquid film thickness under centripetal force.
Goal:
Develop relationship between film thickness and time.
We will consider the problem of fluid retention on a spinning disk and construct a relationship between time and film thickness under a set of simplifying assumptions.
Middleman, Introduction to Fluid Dynamics

15. The Spinning Disk Problem
Assumptions
Axisymmetric flow of fluid across the wafer
Laminar flow of the thinning film
Film thickness decreases slowly with time
Angular velocity of fluid is equivalent to the angular velocity of the disk
Film is thin and has uniform thickness over the wafer
Newtonian and incompressible fluid
Liquid is not volatile
Middleman, Introduction to Fluid Dynamics

16. The Spinning Disk Problem
Continuity Equation:
Momentum Equation:
The continuity equation can be simplified by considering that the flow is radial with negligible flow in the z direction. Where r is radius, and u is velocity.
The momentum equation can be simplified using the assumption that the angular velocity of the fluid is equal to the angular velocity of the disk we can say that velocity is equal to radius multiplied by the angular velocity of the disk. Substituting we arrive at this equation further simplified.
Middleman, Introduction to Fluid Dynamics

17. The Spinning Disk Problem
By assuming the nonlinear term in the momentum equation is small compared to other terms we are able to solve the resulting equation:
Boundary Conditions:
If we assume that the nonlinear term in the momentum equation is small compared to the other terms. We arrive at this simplified momentum equation.
By applying the following boundary conditions that
There is no shear stress on the free surface
And there is no radial velocity at the center of the wafer
We can write an equation relating the amount of solution on the wafer to the amount of solution leaving the wafer.
Middleman, Introduction to Fluid Dynamics

18. The Spinning Disk Problem
We can now say that the volumetric flow, Q, across the edge of the spinning disk is equal to the rate change of the solution volume on disk:
We can say now that Q, the volumetric flow over the edge of the substrate, is equal to the change in volume on the substrate.
By integrating and applying the assumption that the film height is always uniform across the wafer we are able to solve for film height in terms of time.
Middleman, Introduction to Fluid Dynamics

19. The Spinning Disk Problem
Integrating the previous equation we obtain an expression for film thickness, H, in terms of time, t :
For the given assumptions we can say that the ratio of final height to the initial height is related to the density and viscosity of the fluid, the angular velocity of the spinning disk, the initial height of the film and the amount of time the fluid is spun.
Middleman, Introduction to Fluid Dynamics

20. Model Limitations
This model is limited by the assumptions used to derive equations so it only applies to:
Newtonian and non-volatile liquids
Uniform substrates
Development of more general models is significantly more difficult
When developing a model for non-Newtonian flow it must be considered that the viscosity changes with shear force.

21. Agenda Introduction to spin coating Physics of spin coating
Definition and brief history of spin coating
Uses of spin coating technology
Common spin coating defects
Physics of spin coating
Basic physics behind spin coating
Derivations of common spin coating models
Further work on spin coating in relation to my honors college thesis

22. Honors College Thesis Topic
Model flow of spin coated Newtonian fluid using FEMLab, a finite element modeling program.
Extend the FEMLab model to flow of non-Newtonian and viscoelastic fluids on spin coated wafer.
Verify experimentally that the model is valid by spin coating fluids with relevant properties on 6 in silicon wafers and comparing the resultant film thickness with the predicted film thickness.

23. References
Lawrence, C.J, Zhou, W. “Spin coating of non-Newtonian Fluids”. Journal of Non-Newtonian Fluid Mechanics, 39 (1991)
Middleman, S. An Introduction To Fluid Dynamics. John Wiley and Sons. New York. 1998

24. Questions?